The asymptotically faithful property can be used in this case to construct counterexamples to the coarse Baum–Connes conjecture by either taking groups such that the finite quotients form an expander family [1]} (such as groups with property (T)). It can be used explicitly to comprehensively study sequences of graphs of large girth, which is the example above when the group \(G\)  is taken to be a free group [2]} [3]}. These examples motivate the rest of this text.

